What does s represent?

Answer: Typical residual size around the regression line s (or SEE) is the typical magnitude of the residuals — the spread of points around the fitted line.

Answer: (1.11, 2.49) CI = 1.8 ± 1.725(0.4) = 1.8 ± 0.69 = (1.11, 2.49).

Which study yields a tighter CI for slope?

Answer: Study B (smaller SE) A smaller SE produces a smaller margin of error and a tighter (narrower) confidence interval.

AP Statistics · Topic 9.2

Confidence Intervals for the Slope of a Regression Model Practice

Part of Inference for Quantitative Data: Slopes.(UNC-4.I)

Practice questions

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Sample questions

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Sample 1difficulty 2/5
$A regression output reports s = 4.2 (the standard error of the estimate, or RMSE).$
$What does s represent?$
- A
  $Standard error of intercept$
- B
  $Slope's standard error$
- C
  $Standard deviation of x$
- D
  $Typical residual size around the regression line$
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Why
$s (or SEE) is the typical magnitude of the residuals — the spread of points around the fitted line.$
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Sample 2difficulty 3/5
$A regression with n = 22 has slope 1.8 and SE = 0.4. t* for 90% CI with df = 20 is 1.725.$
$What is the 90% CI?$
- A
  $(1.0, 2.6)$
- B
  $(0.8, 2.8)$
- C
  $(1.11, 2.49)$
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- D
  $(1.4, 2.2)$
Why
$CI = 1.8 \pm 1.725(0.4) = 1.8 \pm 0.69 = (1.11, 2.49).$
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Sample 3difficulty 3/5
$Two studies measure the same relationship; Study A has n = 25 with SE(b) = 0.6, Study B has n = 100 with SE(b) = 0.3.$
$Which study yields a tighter CI for slope?$
- A
  $Study A$
- B
  $Both equal$
- C
  $Study B (smaller SE)$
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- D
  $Cannot determine$
Why
$A smaller SE produces a smaller margin of error and a tighter (narrower) confidence interval.$
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Sample 4difficulty 3/5
$A CI for β has the form$
- A
  $x̄ \pm t*\cdots$
- B
  $b \pm SE$
- C
  $b \pm z*\cdotSE(b)$
- D
  $b \pm t*\cdotSE(b)$
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Why
$Standard t-based CI for slope.$
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Sample 5difficulty 3/5
$The regression output shows SE(slope) = 0.8.$
$What does SE(slope) measure?$
- A
  $Half-width of CI$
- B
  $Standard deviation of residuals$
- C
  $Standard deviation of x$
- D
  $Variability of the slope estimate from sample to sample$
  check_circle
Why
$SE(slope) is the estimated standard deviation of the sampling distribution of b — how much b varies across samples.$
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